First-Order Logic Sentence

A First-Order Logic Sentence is a Logic Sentence within a First-Order Logic System.

• AKA: First-Order Formula, FOL Formula.
• Context:
  • It can contain First-Order Logic Operations.
  • It can contain Logic Functions, such as P(a,x).
  • It can be a member of a First-Order Logic Model.
  • …
• Example(s):
  • [math]\displaystyle{ C }[/math] = P(a,x) ∨ Q(b) ∨ ¬R(x).
  • [math]\displaystyle{ D }[/math] = P(x,a) ∨ Q(x) ∧ P(y,a) ∨ Q(b).
  • …
• Counter-Example(s):
  • a Markov Logic Network.
• See: Propositional Logic Sentence, First-Order Logic Inference Task, First-Order Sentence Satisfiability Task, Default Logic Rule.

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References

2009

• (Domingos & Lowd, 2009) ⇒ Pedro Domingos, and Daniel Lowd. (2009). “Markov Logic: An Interface Layer for Artificial Intelligence." Morgan & Claypool. doi:10.2200/S00206ED1V01Y200907AIM007
  • QUOTE: A first-order knowledge base (KB) is a set of sentences or formulas in first-order logic [37]. Formulas are constructed using four types of symbols: constants, variables, functions, and predicates. Constant symbols represent objects in the domain of interest (e.g., people: Anna, Bob, Chris, etc.). Variable symbols range over the objects in the domain. Function symbols (e.g., MotherOf) represent mappings from tuples of objects to objects. Predicate symbols represent relations among objects in the domain (e.g., Friends) or attributes of objects (e.g., Smokes). An interpretation specifies which objects, functions and relations in the domain are represented by which symbols.

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